The question particle described in the book cited is “μήπως” (page 301). But μήπως is very rarely used. I’d say questions are formed by intonation change, and usually (but not always) there is an interrogative world order where the verb is placed first.
It’s not the first time this site has wrong information about the greek language.

The mention of the question particle is not really an error. The chapter states explicitly:” In some languages, intonation may be the most common means of indicating a polar question, but if some other method is used a minority of the time, then the language is shown on the map according to that method.” Both Joseph & Philippaki-Warburton (1987: 4) and Mackridge (1985: 235) are explicit in saying that the word order is the same in interrogative sentences. Holton et al (2012: 503) note that verb-initial word order is common in polar questions, but since this order is not obligatory in questions and also common in declarative sentences, it is not clear that we can say that polar questions are signaled by word order. Hence, the coding of this datapoint is not incorrect.

In greek, the method used to indicate a question is intonation which exists always. The particle μήπως is not only very rarely used, it is a word that actually changes the meaning of the question. It indicates doubt, insecurity, wondering. Wiktionary explains quite well how it is used. But anyway, you say that “if some other method is used a minority of the time..” . Well, the change of the word order is used a minority (or majority) of time, but you dismiss it without explaining why. Where is it written that if the different word order is not used exclusively in questions, it doesn’t count?

And why is “que” f.ex. not considered a question particle in catalan?

But the main problem with your classification is that it is based on arbitrary definitions, one could say thar it is practically meaningless, a play of words. You start the text saying that “This map shows the method a language uses to indicate that an utterance is a polar question.” Well, μήπως is not the method the greek language uses to indicate that an utterance is a polar question. It’s not a coincidence that 3 native speakers are saying it sounds wrong.

Even if μήπως is considered a question particle, I wouldn’t have placed greek in the same category with turkish, mandarin, finnish or irish where its use is obligatory. But, it’s your map, your rules.